Transferring monotonicity in weighted norm inequalities.

Sinnamon, Gord. "Transferring monotonicity in weighted norm inequalities.." Collectanea Mathematica 54.2 (2003): 181-216. <http://eudml.org/doc/43083>.

@article{Sinnamon2003,
abstract = {Certain weighted norm inequalities for integral operators with non-negative, monotone kernels are shown to remain valid when the weight is replaced by a monotone majorant or minorant of the original weight. A similar result holds for operators with quasi-concave kernels. To prove these results a careful investigation of the functional properties of the monotone envelopes of a non-negative function is carried-out. Applications are made to function space embeddings of the cones of monotone functions and quasi-concave functions. Under weaker partial orders on non-negative functions, monotone envelopes are re-examined and the level function is recognized as a monotone envelope in two ways. Using the level function, monotonicity can be transferred from the kernel to the weight in inequalities restricted to a cone of monotone functions.},
author = {Sinnamon, Gord},
journal = {Collectanea Mathematica},
keywords = {Desigualdades; Espacios de funciones medibles; Monotonicidad; Funciones de peso; quasi-concave functions; monotonicity; weight; inequalities},
language = {eng},
number = {2},
pages = {181-216},
title = {Transferring monotonicity in weighted norm inequalities.},
url = {http://eudml.org/doc/43083},
volume = {54},
year = {2003},
}

TY - JOUR
AU - Sinnamon, Gord
TI - Transferring monotonicity in weighted norm inequalities.
JO - Collectanea Mathematica
PY - 2003
VL - 54
IS - 2
SP - 181
EP - 216
AB - Certain weighted norm inequalities for integral operators with non-negative, monotone kernels are shown to remain valid when the weight is replaced by a monotone majorant or minorant of the original weight. A similar result holds for operators with quasi-concave kernels. To prove these results a careful investigation of the functional properties of the monotone envelopes of a non-negative function is carried-out. Applications are made to function space embeddings of the cones of monotone functions and quasi-concave functions. Under weaker partial orders on non-negative functions, monotone envelopes are re-examined and the level function is recognized as a monotone envelope in two ways. Using the level function, monotonicity can be transferred from the kernel to the weight in inequalities restricted to a cone of monotone functions.
LA - eng
KW - Desigualdades; Espacios de funciones medibles; Monotonicidad; Funciones de peso; quasi-concave functions; monotonicity; weight; inequalities
UR - http://eudml.org/doc/43083
ER -